\documentclass{amuc}
\usepackage{amsfonts}
\begin{document}

%% \title[HEADLINE TITLE]{LONG TITLE \\ WITH TWO LINES}
%% The part [] is optional and can be deleted, if the title is short

\title[TITLE OF ARTICLE]{THE LONG TITLE OF THE VERY CRAZY ARTICLE \\
OR HOW TO USE AMUC.CLS}

%% First author ...name + address + email
%% \author{F. Second_name}
%% \address{Street XY, Town, State}
%% \curraddr{...}
%% current address, e-mail and url are optional
%% \email{...@...}
%% \urladdr{...}

\author{F. Anonymous}
\address{Fun street 26, 876 67 Fun, Funland}
\curraddr{Sun street, Sunland}
\email{fanonymous@fun.xy}
\urladdr{http://www.anonymous.com/~anonymous}

%% If there are more authors, then second author, third author contains
%% the same items

\author{S. Anonymous}
\address{University of \dots, }

%% (optional) If any thanks for the financial supports, grants, ...
%\thanks{The first  author was supported  ...}

\thanks{The authors gratefully
acknowledge the financial support from the project XY}

%% (optional) Keywords

\keywords{fun, amuc}

%% (obligatory) AMS Classification 2000
%% The Primary classification is obligatory,
%% the Secondary classification is optional.
%% \subjclass{primary}{secondary}
%% f.e. \subjclass{35R35, 49M15, 49N50}{} or \subjclass{35R35, 49M15}{49N50}

\subjclass{35R35, 49M15, 49N50}{}

%% (optional) Abstract
\begin{abstract}
This article describes simply how to use amuc.cls.
\end{abstract}

\maketitle


%%%%% private macros, f.e. the different environments
\newtheorem{theorem}{Theorem}[section]
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{defn}[theorem]{Definition}
%%% for unnumbered environments, use:
\newtheorem*{remark}{Remark}
%%% for no-italic, numbered environments, use:
\newenvironment{definition}{\begin{defn}\normalfont}{\end{defn}}

%%%% the main article

\section{First section}

The article can be written the same way as  the standard article.cls
or more precisely amsart.cls. It means, the environments as
\begin{verbatim}
\begin{align}...\end{align}
\begin{align*}...\end{align*}
...
\end{verbatim}
can also be used.

{\bfseries The
 bold style} is used for emphasized words.

 If you need to use mathematical symbols as
$\mathbb{R}$,  use
\begin{verbatim}
\usepackage{amsfonts}
\end{verbatim}
at the beginning of the document and use the standard macros as
{\ttfamily \char'134mathbb\{...\}}.

\subsection{First subsection}

\begin{theorem}[Fermat]\label{main}
The first theorem \dots -- the theorems are written in italic style.
\end{theorem}

\begin{theorem}
The second theorem \dots
\end{theorem}

\begin{definition}
In the journal, the definitions and remarks are not written in italic style.
\end{definition}

\begin{lemma}
The lemma -- again in italic style.
\end{lemma}


\begin{proof}
The environment ``proof'' is defined automatically.
\end{proof}


\begin{proof}[Proof of Theorem~{\upshape\ref{main}}]
The environment ``proof'' is defined automatically and the word ``Proof'' can be changed
as optional argument.
\end{proof}

\begin{proof*}
The environment ``proof'' with the star is also defined automatically and it can
be use, when the symbol $\Box$ for ``end proof'' should not be  given.
\end{proof*}


\begin{remark}
You can also very simply to define unnumbered environments.
\end{remark}

\begin{acknowledgment}[Acknowledgement]
Thank you Peter Pan for helpful comment to this article.
\end{acknowledgment}

% or it can be used also as \begin{acknowledgment}[Acknowledgments]


%%%% references
\begin{thebibliography}{9}

\bibitem{russo1}
Russo D., Bresler E., Shani U. and  Parker J. C.,
{\em Analysis of infiltration events in relation to determining soil
hydraulic properties by inverse problem methodology},
 Water Resources Research {\bf27} (1991), 1361--1373.

\bibitem{russo2}
\bysame,
{\em Analysis of \dots}, \dots, 177--199.

\end{thebibliography}

\end{document}
